My telescope's sidereal tracking is lousy: it just doesn't work. To overcome this, when taking long-exposure photographs through it, what's the best way to reduce star trailing?
Sounds like you should get a new mount. :-)
Being more serious, even expensive mounts have periodic tracking errors (due to manufacturing tolerance of gears and moving equipment) that need to be corrected. These are the basic ways to do the corrections:
- Add a guide scope to the side of your scope, use an eyepiece with cross-hairs, and watch a star while you take a photo. When the scope drifts, you push buttons to move the scope to keep the star centered.
- Do the same thing with a guide scope but use a dedicated guide camera that provides the corrections to the tracking.
- There are also guide cameras that you can insert just in front of the camera. They use a small "pick-off" mirror to look at a star in the field (off axis guider). The guide camera provides the corrections to the tracking.
Of course, all of these methods require a mount that can be moved slowly and smoothly in both right-ascension and declination to keep the guide star centered. Also, the mount needs to be an equatorial mount and accurately aligned. (More expensive mounts can be alt-azimuth mounts and use a gadget to rotate the camera during the exposure.)
This is not quite a full answer, but a useful addition to your image processing stack are deconvolution methods designed with astronomy in mind.
There's a free software tool for image processing called Iris which includes some useful deconvolution methods not available in typical image processing applications.
Here's a brief tutorial showing what's possible with these tool. Note in particular the RL2 method, rather than the RL method.
Note that these tool should not be used generally to correct long exposure star trails, but can correct small trails.